Discussion
An alternating voltage is given by v=20 sin (157t), the frequency of the alternating voltage is :
Answer: C
The frequency is 25 Hz.
An alternating voltage written as \(v = V_{m}\sin(\omega t)\) has angular frequency \(\omega = 2\pi f\). Here \(\omega = 157\) rad/s.
\[ \begin{aligned} f &= \frac{\omega}{2\pi} = \frac{157}{2 \times 3.14} \\ &= \frac{157}{6.28} = 25\ \text{Hz} \end{aligned} \]
50 Hz would need \(\omega = 314\) rad/s, and 100 Hz 628 rad/s. 75 Hz does not correspond to 157 rad/s at all.
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